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Set Theory

Set Theory. A2 Set Functions. Set Functions. Everything together. What they have the SAME. What is NOT in the set (cross out). Examples. 1. Given P = {1, 3, 5, 7, 9} and Q = {0, 2, 4, 6, 8}, find Intersection of P and Q ___________________ Union of P and Q ________________________.

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Set Theory

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  1. Set Theory A2 Set Functions

  2. Set Functions Everything together What they have the SAME What is NOT in the set (cross out)

  3. Examples 1. Given P = {1, 3, 5, 7, 9} and Q = {0, 2, 4, 6, 8}, find Intersection of P and Q ___________________ Union of P and Q ________________________ { } Do NOT write 0! { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 } What they have the SAME Everything together No They have nothing the same Need to write it in ORDER This is called the Empty set

  4. Examples 2. Given A = {0, 2, 4, 6, 8, 10} B = {0, 2, 3, 5, 6} C = {0, 1, 2, 3, 4, 5} • What is A∩B? _________________________ b. What is A∩B∩C? ________________________ c. What is BUC? ___________________________ d. What is AUB? ___________________________ { 0 , 2 , 6 } { 0 , 2 } { 0 , 1 , 2 , 3 , 4 , 5 , 6 } { 0 , 2 , 3 , 4 , 5 , 6 , 8 , 10 }

  5. Examples X X X X 3. Given: Set U = {1, 2, 3, 4, 5, 6, 7, 8} Set B = {2, 3, 5, 6} Set B is a subset of set U, what is the compliment of set B? a. { } c. {2, 3, 5, 6} b. {1, 4, 7, 8} d. {1, 2, 3, 4, 5, 6, 7, 8} What is NOT in the set Cross out everything that is in the SUBSET What is left?

  6. 4. Given: A = {all even integers from 2 through 20, inclusive} B = {2, 6, 10, 14, 16} What is the complement of set B within set A? a. {2, 6, 10, 14, 16} • {4, 8, 12, 18} • {4, 8, 12, 18, 20} d. {2, 4, 6, 8, 10, 12, 14, 16, 18, 20} 2 X 4 6 X 8 10 X 12 14 X 16 X 18 20

  7. Examples 5. Given Find the intersection of A and B ___________ Find A U C ____________________________ Find the intersection of A, B, and C __________ { 1, 2, 3} { 1, 2, 3, 4, 5, 6, 7, 9} { 1, 3} What they have the SAME Union What they have the SAME Everything together Everything that is blue

  8. Examples 6. Maureen tracks the range of outdoor temperatures over three days. She records the following information. Express the intersection of the three sets as an inequality in terms of temperature t _______________ 0 ≤ ≤ t 40 What they have the SAME Do they all have 0? Do they all have 40? Do they all have 45? Do they all have 50? Do they all have -20? Do they all have -23? No Yes Yes No No No

  9. Practice Problems Now try the practice problems on your own

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